Example: cylinder

Note

You can launch an interactive, editable version of this example without installing any local files using the Binder service (although note that at some times this may be slow or fail to open):

A short cylinder with constant injection at one end.

from brian2 import *

defaultclock.dt = 0.01*ms

# Morphology
diameter = 1*um
length = 300*um
Cm = 1*uF/cm**2
Ri = 150*ohm*cm
N = 200
morpho = Cylinder(diameter=diameter, length=length, n=N)

# Passive channels
gL = 1e-4*siemens/cm**2
EL = -70*mV
eqs = '''
Im = gL * (EL - v) : amp/meter**2
I : amp (point current)
'''

neuron = SpatialNeuron(morphology=morpho, model=eqs, Cm=Cm, Ri=Ri,
                       method='exponential_euler')
neuron.v = EL

la = neuron.space_constant[0]
print("Electrotonic length: %s" % la)

neuron.I[0] = 0.02*nA # injecting at the left end
run(100*ms, report='text')

plot(neuron.distance/um, neuron.v/mV, 'kx')
# Theory
x = neuron.distance
ra = la * 4 * Ri / (pi * diameter**2)
theory = EL + ra * neuron.I[0] * cosh((length - x) / la) / sinh(length / la)
plot(x/um, theory/mV, 'r')
xlabel('x (um)')
ylabel('v (mV)')
show()